Mathematical Formulas for Industrial and Mechanical Engineering

3 Linear Algebra

Linear algebra is the branch of mathematics concerning vector spaces, often finite

or countable infinite dimensional, as well as linear mappings between such spaces.

Such an investigation is initially motivated by a system of linear equations in sev-

eral unknowns. Such equations are naturally represented using the formalism of

matrices and vectors. Linear algebra is central to both pure and applied mathemat-

ics. For instance, abstract algebra arises by relaxing the axioms of a vector space,

leading to a number of generalizations. Functional analysis studies the infinite-

dimensional version of the theory of vector spaces. Combined with calculus, linear

algebra facilitates the solution of linear system s of differential equations. ...